When vehicle dynamics control systems are used in motor vehicles and mobile machines, the tire slip, also referred to as λ, is a key state variable of great importance. This state variable is necessary for slip control in antilock braking systems (ABS) and traction control systems (TCS). In these types of systems and controls, the object of control is to minimize an absolute difference between an actual slip acting on the particular wheel and a desired setpoint slip. The setpoint slip is computed in an appropriate controller. If only an ABS is used, a so-called instability controller may also be used.
This tire slip is also used as a control variable in commonly used electronic stability program (ESP) systems. A vehicle controller in the electronic stability program relies on a subordinate ABS and/or ASR slip controller.
Tire slip λ is computed from free-running wheel speed νfree and actual wheel speed νactual according to the formula:
  λ  =                    (                              ν            free                    -                      ν            actual                          )                    v        free              .  
Actual wheel speed νactual may be computed from wheel radius r and actual wheel speed Ωactual. This computation is carried out according to the formula νactual=r·Ωactual.
Free-running wheel speed νfree may be ascertained using a free-running wheel speed Ωfree and the wheel radius according to νfree=r·Ωfree.
The free-running wheel speed is understood to mean the rotational speed which a wheel experiences solely by rolling on a road surface without being decelerated or accelerated.
Free-running wheel speed Ωfree is also frequently referred to as “wheel reference speed” in the literature.
However, it is precisely this wheel reference speed or free-running wheel speed Ωfree which is ultimately needed in the computation
      λ    =                            r          ·                      Ω            free                          -                  (                      r            ·                          Ω              actual                                )                            r        ·                  Ω          free                      ,which results in the tire slip. After rearrangement of the equation, λ may be computed according to the following formula:
  λ  =      1    -                  (                              Ω            actual                                Ω            free                          )            .      
The actual wheel speed present during motion, i.e., during deceleration as well as acceleration of the wheel, is measured by wheel speed sensors which are present on each wheel. If the wheel is not accelerated or decelerated, the wheel runs freely in the sense that it rolls unimpeded on the road surface, thus allowing the wheel speed sensors to be used for determining the free-running wheel speed.
When the wheel runs, i.e., rolls, freely, Ωactual is equal to Ωfree. By using the value Ωactual for the free-running wheel, free-running wheel speed νfree may be ascertained by multiplying it by the wheel radius. This is possible because the slip is equal to zero when the wheel is freely rolling.
However, when the vehicle is accelerated or decelerated, one or more of the wheels are frequently in slip; i.e., they completely or partially slip. Other methods must then be used to allow the free-running wheel speed to be ascertained. Hydrostatic drives are commonly used in mobile machines as well as in other motor vehicles. These hydrostatic drives operate using transfer media for transmitting kinetic energy. As a rule mineral oils are used, although environmentally acceptable liquids such as water or specialized esters or glycols are finding increasing use. Hydrostatic drives have the advantage that in terms of energy they allow an essentially optimal type of gear transmission, since continuous adjustment of the speed on the drive side is possible.
A method and a device are known from DE 199 18 882 A1 for providing a control assistance and traction control system for hydrostatically driven vehicles. This document discloses a hydraulically driven vehicle having a front pair and a rear pair of wheels. An oscillating motor acts on each wheel, and is adjustable in such a way that it may be swiveled into a pump mode. The oscillating motor actively accelerates the particular wheel, whereas after switching to pump mode the oscillating motor appropriately decelerates the particular wheel. The rotational speed of the wheel is ascertained with the aid of wheel speed sensors mounted near the wheel.
As also disclosed in DE 199 18 882 A1, for hydrostatic drives deceleration is performed either exclusively or partially with the aid of the oscillating motors, also referred to as adjusting motors, due to the fact that the oscillating motors function as a pump and adapt to the oil pressure which develops from driving the pump and an adjoining internal combustion engine.
To intensify the deceleration effect it is common to use power brakes, for example mechanical service/parking brakes.
To ascertain the reference speed and/or the free-running wheel speed, an estimate is usually made by averaging the individual signals of the wheel speed sensors, which is performed on an arithmetic or weighted basis. This estimate is then further optimized using a corrective “vehicle model.” This vehicle model takes into account, for example, the steering angle and the particular acceleration or deceleration of the vehicle. The particular measured minima and maxima of Ωactual are ascertained for all wheels, for example all four wheels. Depending on the brake or traction control, the minima or maxima are selected and compared to one another by forming the median or mean. Support models which take into account the road surface, for example asphalt or ice, are then used.
In the case of acceleration, the rotational speed is limited by forming a maximum, i.e., the maximum possible acceleration. In the case of deceleration, the rotational speed is limited by forming a minimum, i.e., the maximum possible deceleration.
However, if all four wheels or individual wheels are clearly in slip, this conventional method results in an erroneous value for Ωfree. The vehicle is then necessarily under- or overbraked. The handling capability of the vehicle is reduced while passing another vehicle, which in some cases may even result in accidents.